A few things will happen that will compete to kill us, and yes we’ll all die very quickly, but sadly we won’t get eaten by the black hole.
A popular misconception about black holes is that they’re cosmic vacuum cleaners eating everything in their vicinity. Well, they surely do attempt to, but they have a tiny stomach. The problem isn’t when they eat. It’s when they vomit because of too much food. THAT tends to be very destructive.
So it’s rather complex actually. We can estimate a few things quickly since the radius of a black hole is proportional to the mass.
Lets do a few calculations!
As per the assumption, a black hole with a Schwarzschild radius (as has been noted) would have a mass of 7×10^23 kg, more than the mass of 5 moons combined.
The ratio of Earth to Sun mass is 3 parts in 1 million. Thus, if the Earth were a black hole it would have a radius of 9 millimeters.
That means a 1 mm black hole has a mass about 11% of the earth. We would certainly have a problem from an 11% additional mass at the Earth.
Significant enough that the overall gravity of the Earth would increase noticeably. This additional increase in gravity would be sufficient to alter the Moon’s orbit. This could cause the Moon to sling shot out of orbit to follow an elliptical path contrasting to its original path.
Where is this putative micro black hole placed – at the surface, in the center, revolving ?
Assuming the 1 mm micro black hole placed on the Earth surface , its sphere of influence would have a radius of about 1/3rd of the earth radius.
All the matter in that immediate vicinity would feel a stronger gravity from the black hole and would consume everything while falling toward the center of the earth. The time scale to fall towards the center would be close to 42 minutes.
It would revolve in around the earth’s center for a while and pass through the core in about the same time reaching the other side of the earth surface.
Also, if the black hole appeared on the surface with a relative velocity of less than 12 km/s, it will orbit the earth along with its sphere of influence. That means the destruction of the earth’s crust and most of its mantle. Simply, the death of everything living on its surface.
Accretion rate and Eddington Luminosity
A significant fraction of the earth mass surrounding black hole becomes available food to be accreted by the black hole. However, this material has to lose all of its angular momentum before it will simply fall in, so it starts swirling its way to the black hole forming an accretion disc.
This material produces a lot of heat that will be radiated away. Radiation has a pressure which will limit further accretion. The two effects will balance each other at what is called Eddington luminosity.
There’s also a hard limit to the black hole accretion rate in the form of the Eddington luminosity. The little accretion disk would probably have a temperature about 6000 K ,similar to Earth’s core or about Sun’s surface temperature.
There would be some frictional processes between the accretion disk and the Earth’s bulk that would cause the micro black hole to settle toward the core over time.
Long things short
Basically, it would take 5 billion years for your black hole to eat the Earth. It would certainly raise the mass of the Earth significantly. It would immediately cause major disruption throughout the planet, and within no more than a few hours, the entire planet would be an uninhabitable mess of collapsing crust, lava, hot gases, whatever.
Life would become unsustainable and the black hole’s heavy mass could even disrupt the asteroid belt. This could lead to frequent collision for a million years in the solar system. Moon will continue to revolve around the New Earth (Black hole) but in an highly elliptical orbit.
The black hole will not directly go to earth’s center but will revolve in about the earth’s center for a while and then reach its center which is much more creepier. The details of how it would grow would require a complex simulation and calculation.
For more reference, check out this amazing video from Kurzgesagt.